diff --git a/poincare/include/poincare/hyperbolic_arc_cosine.h b/poincare/include/poincare/hyperbolic_arc_cosine.h
index f4a6ef928..c49ca9617 100644
--- a/poincare/include/poincare/hyperbolic_arc_cosine.h
+++ b/poincare/include/poincare/hyperbolic_arc_cosine.h
@@ -20,6 +20,8 @@ public:
   // Properties
   Type type() const override { return Type::HyperbolicArcCosine; }
 private:
+  // Simplification
+  bool isNotableValue(Expression e) const override { return e.isRationalOne(); }
   // Layout
   Layout createLayout(Preferences::PrintFloatMode floatDisplayMode, int numberOfSignificantDigits) const override;
   int serialize(char * buffer, int bufferSize, Preferences::PrintFloatMode floatDisplayMode, int numberOfSignificantDigits) const override;
diff --git a/poincare/include/poincare/hyperbolic_cosine.h b/poincare/include/poincare/hyperbolic_cosine.h
index 749540b8e..efd9e632d 100644
--- a/poincare/include/poincare/hyperbolic_cosine.h
+++ b/poincare/include/poincare/hyperbolic_cosine.h
@@ -20,6 +20,8 @@ public:
   // Properties
   Type type() const override { return Type::HyperbolicCosine; }
 private:
+  // Simplification
+  Expression imageOfNotableValue() const override { return Rational::Builder(1); }
   // Layout
   Layout createLayout(Preferences::PrintFloatMode floatDisplayMode, int numberOfSignificantDigits) const override;
   int serialize(char * buffer, int bufferSize, Preferences::PrintFloatMode floatDisplayMode, int numberOfSignificantDigits) const override;
diff --git a/poincare/include/poincare/hyperbolic_trigonometric_function.h b/poincare/include/poincare/hyperbolic_trigonometric_function.h
index 798beb928..62a896c49 100644
--- a/poincare/include/poincare/hyperbolic_trigonometric_function.h
+++ b/poincare/include/poincare/hyperbolic_trigonometric_function.h
@@ -3,10 +3,12 @@
 
 #include <poincare/expression.h>
 #include <poincare/trigonometry.h>
+#include <poincare/rational.h>
 
 namespace Poincare {
 
 class HyperbolicTrigonometricFunctionNode : public ExpressionNode {
+  friend class HyperbolicTrigonometricFunction;
 public:
   // TreeNode
   int numberOfChildren() const override { return 1; }
@@ -15,12 +17,16 @@ private:
   LayoutShape leftLayoutShape() const override { return LayoutShape::MoreLetters; };
   LayoutShape rightLayoutShape() const override { return LayoutShape::BoundaryPunctuation; }
   Expression shallowReduce(ReductionContext reductionContext) override;
+  virtual bool isNotableValue(Expression e) const { return e.isRationalZero(); }
+  virtual Expression imageOfNotableValue() const { return Rational::Builder(0); }
 };
 
 class HyperbolicTrigonometricFunction : public Expression {
 public:
   HyperbolicTrigonometricFunction(const HyperbolicTrigonometricFunctionNode * n) : Expression(n) {}
   Expression shallowReduce(ExpressionNode::ReductionContext reductionContext);
+private:
+  HyperbolicTrigonometricFunctionNode * node() const { return static_cast<HyperbolicTrigonometricFunctionNode *>(Expression::node()); }
 };
 
 }
diff --git a/poincare/src/hyperbolic_trigonometric_function.cpp b/poincare/src/hyperbolic_trigonometric_function.cpp
index c502760d8..adcb252ff 100644
--- a/poincare/src/hyperbolic_trigonometric_function.cpp
+++ b/poincare/src/hyperbolic_trigonometric_function.cpp
@@ -17,18 +17,23 @@ Expression HyperbolicTrigonometricFunction::shallowReduce(ExpressionNode::Reduct
   }
 
   Expression thisExpression = *this;
-
-  // Step 1. Map on matrix child if possible
   Expression c = childAtIndex(0);
-  if (childAtIndex(0).type() == ExpressionNode::Type::Matrix) {
+
+  // Step 0. Map on matrix child if possible
+  if (c.type() == ExpressionNode::Type::Matrix) {
     return mapOnMatrixFirstChild(reductionContext);
   }
 
-  // Step 2. TODO EMILIE ?? Try finding an easy standard calculation reduction
+  // Step 1. Notable values
+  if (node()->isNotableValue(c)) {
+    Expression result = node()->imageOfNotableValue();
+    replaceWithInPlace(result);
+    return result;
+  }
 
-  // Step 3. Look for an expression of type "cosh(acosh(z))", return z
+  // Step 2. Look for an expression of type "cosh(acosh(z))", return z
   ExpressionNode::Type t = type();
-  ExpressionNode::Type childT = childAtIndex(0).type();
+  ExpressionNode::Type childT = c.type();
   {
     Expression result;
     if (t == ExpressionNode::Type::HyperbolicCosine) {
@@ -90,7 +95,7 @@ Expression HyperbolicTrigonometricFunction::shallowReduce(ExpressionNode::Reduct
     }
   }
 
-  // Step 4. Look for an expression of type "cosh(-x)", return "+/-cosh(x)"
+  // Step 3. Look for an expression of type "cosh(-x)", return "+/-cosh(x)"
   if (t != ExpressionNode::Type::HyperbolicArcCosine) {
     Expression positiveArg = childAtIndex(0).makePositiveAnyNegativeNumeralFactor(reductionContext);
     if (!positiveArg.isUninitialized()) {
diff --git a/poincare/test/simplification.cpp b/poincare/test/simplification.cpp
index 6b73a0c3d..d9e22fc9d 100644
--- a/poincare/test/simplification.cpp
+++ b/poincare/test/simplification.cpp
@@ -597,6 +597,15 @@ QUIZ_CASE(poincare_simplication_trigonometry_functions) {
   assert_parsed_expression_simplify_to("tan(asin(-x))", "-x/√(-x^2+1)", User, Degree);
 }
 
+QUIZ_CASE(poincare_simplication_hyperbolic_trigonometry_functions) {
+  assert_parsed_expression_simplify_to("sinh(0)", "0");
+  assert_parsed_expression_simplify_to("cosh(0)", "1");
+  assert_parsed_expression_simplify_to("tanh(0)", "0");
+  assert_parsed_expression_simplify_to("asinh(0)", "0");
+  assert_parsed_expression_simplify_to("acosh(1)", "0");
+  assert_parsed_expression_simplify_to("atanh(0)", "0");
+}
+
 QUIZ_CASE(poincare_simplication_matrix) {
   // Addition Matrix
   assert_parsed_expression_simplify_to("1+[[1,2,3][4,5,6]]", Undefined::Name());
@@ -699,11 +708,11 @@ QUIZ_CASE(poincare_simplification_functions_of_matrices) {
   assert_parsed_expression_simplify_to("gcd(1,[[0,180]])", Undefined::Name());
   assert_parsed_expression_simplify_to("gcd([[0,180]],[[1]])", Undefined::Name());
   assert_parsed_expression_simplify_to("acosh([[0,π]])", "[[acosh(0),acosh(π)]]");
-  assert_parsed_expression_simplify_to("asinh([[0,π]])", "[[asinh(0),asinh(π)]]");
-  assert_parsed_expression_simplify_to("atanh([[0,π]])", "[[atanh(0),atanh(π)]]");
-  assert_parsed_expression_simplify_to("cosh([[0,π]])", "[[cosh(0),cosh(π)]]");
-  assert_parsed_expression_simplify_to("sinh([[0,π]])", "[[sinh(0),sinh(π)]]");
-  assert_parsed_expression_simplify_to("tanh([[0,π]])", "[[tanh(0),tanh(π)]]");
+  assert_parsed_expression_simplify_to("asinh([[0,π]])", "[[0,asinh(π)]]");
+  assert_parsed_expression_simplify_to("atanh([[0,π]])", "[[0,atanh(π)]]");
+  assert_parsed_expression_simplify_to("cosh([[0,π]])", "[[1,cosh(π)]]");
+  assert_parsed_expression_simplify_to("sinh([[0,π]])", "[[0,sinh(π)]]");
+  assert_parsed_expression_simplify_to("tanh([[0,π]])", "[[0,tanh(π)]]");
   assert_parsed_expression_simplify_to("im([[1/√(2),1/2][1,-1]])", "[[0,0][0,0]]");
   assert_parsed_expression_simplify_to("im([[1,1+𝐢]])", "[[0,1]]");
   assert_parsed_expression_simplify_to("int([[0,180]],x,1,2)", Undefined::Name());